Detection depends on the frequency of your weather radar. If it operates on the same frequency as any Soviet equipment, then it should be in the correct range!
The SOP for jets fitted with RWR/RHWR is to fly around with them switched on to help detect other platforms with RF emitters. Additionally, when not using our own radar for anything specific, it is selected to wide scan to aid our own conspicuity and help fry our nuts good and proper.
I would suggest that flying with your weather radar switched on is probably the way ahead unless you have a good reason not to. If it is switched on, there is a small chance it may aid others detect your presence.